Granger Granger Granger M1 ECM M1 M1 20 90 1 2005
2004 10 12 7 2004 11 10 2004 11 17
Vasicek(1977) Dothan (1978) Courtadon (1982) Cox Ingersoll and Ross (1985) Chan Karolyi Longstaff and Sanders (1992) Svensson (1994) Hull and White (1993) Heath Jarrow and Morton (1992) Black Derman and Toy (1990) Hull and White (1990) and Black & Karasinski (1991) Stanton (1997) Angelini 1990
Barro 1992 Mankiw Miron 1993 2002 Vasicek CIR 2003 2004 2005 2005 Granger 2005 GARCH
VAR Grange GDP 1993 2005 50 1.
1979 20 2004 27787 GDP 20.1% 1994-1996 2000 2004 381.6 1.37% 1 1984 2003 4113.4 1996 4.11 2003 1 7 94.43% 2003 2
proxy variable 7 7 1993 2001 1993 1.3 1994 1996 20021993 1995 1996 2005 7 2. GDP GDP (CPI) (RPI)
M0 M1 + M2 M1+ + + M0 M1 M2 1 3. GDP M0 M1 M2 X11 X12 X11
GDP X-11 GDP 1. DF ADF Philips (PP ) ADF PP AIC SC
ADF 1 PP 5 GDP M0 M1 M2 RPI 5 1 ADF 5 1 PP 5 I(1) 2. Granger Granger Granger 10 Granger 10 Granger 10 GDP CPI RPI Granger
( ) 3. EG Johansen Gregory Hansan 1996 ( ARDL) Bayes Engle Granger Johansen 1988 (MLE) Gonzalo Johansen Engle Granger Johansen AIC SC ( ) Johansen SC AIC Granger
0 0 LNI =0.3335LNGDP +18.7032LNCPI +3.4267 LND - (0.19700) (4.14103) (0.77058) 1.2136LNL - 4.7658LNM0+3.0332 LNM1 (0.79210) (0.58273) (0.87978) +1.4096 LNM2-1.6076 LNER -0.0883 DI +0.0718 LI (0.38240) (0.32539) (0.04971) (0.05158) -13.095LNRPI -0.1736@TREND(93:2)-47.49145 (4.59565) (0.02860) (1) LNGDP DI LI LNI LNCPI LNRPI LNCPI
Granger LND LNL LNGDP DI LI LNL LNRPI 1 3 LNM0 LNM1 M0 M1 M2 LNM0 LNM2 1 4
LNM1 LND LND LNM1 1 2 4 4 3 3 1.0 0.5 0.0 2 1 0 1.0 0.5 0.0 2 1 0-0.5-0.5-1.0 93 94 95 96 97 98 99 00 01 02 03 04 05 Residual Actual Fitted -1.0 93 94 95 96 97 98 99 00 01 02 03 04 05 Residual Actual Fitted 1 10.1 M1 1 0.31 1 17 3( Residual Actual Fitted ) LND LNM1
LND LNM1 Johansen 1 3 1 29.3 1 54.5 1 0.6 4 4. Granger VAR MA ECM VAR ECM ECM
4 3 6 ECt =LNIt-16.69*LNCPI t+668.9*lner t+0.405*lnm1t-1341.779
R2=0.622435; =-0.04591; =0.093314; =0.074319; AIC=-2.06602; SC=-1.328775; =0.13808; =62.41946; DW=2.122966; F =2.424344; P=0.021671; R2 SE DW 1993 1 2005 2 5 0.2 0.1 0.0-0.1 0.2 0.0-0.2-0.4 3.0 2.5 2.0 1.5 1.0 0.5 Forecast: LNIF A ctual: LNI Forecast sample: 1993:1 2005:2 A djusted sample: 1994:4 2005:2 Included observations: 43 Root Mean S quared E rror 0.056668 Mean A bs. P ercent E rror 0.038717 Mean A bsolute P ercentage E rror 4.191928 Theil Inequality Coefficient 0.017447 B ias P roportion 0.000000 V ariance P roportion 0.000452-0.2 95 96 97 98 99 00 01 02 03 04 05 Residual Actual Fitted 0.0 95 96 97 98 99 00 01 02 03 04 05 LN IF?2 S.E.
R 2 R 2 1993 1 2005 2 7 0.2 0.1 0.0-0.1 3.0 2.5 2.0 1.5 1.0 0.5 0.0 3.0 2.5 2.0 1.5 1.0 0.5 Forecast: LN IF A ctual: LNI Forecast sample: 1993:1 2005:2 A djusted sample: 1993:3 2005:2 Included observations: 48 R oot Mean S quared E rror 0.075269 Mean A bs. P ercent E rror 0.054685 Mean A bsolute P ercentage E rror 4.863257 Theil Inequality C oefficient 0.021708 B ias P roportion 0.000000 V ariance P roportion 0.002403-0.2-0.3 94 95 96 97 98 99 00 01 02 03 04 05 Residual Actual Fitted 0.0 94 95 96 97 98 99 00 01 02 03 04 05 LN IF?2 S.E.
(Chow)F : 2 CUSUM N CHOW 5 VAR 5. VEC 1 9 1
0.12 0.08 0.04 0.00-0.04 1 2 3 4 5 6 7 8 9 10 0.12 0.08 0.04 0.00-0.04 1 2 3 4 5 6 7 8 9 10 0.12 0.08 0.04 0.00-0.04 1 2 3 4 5 6 7 8 9 10 0.12 0.08 0.04 0.00-0.04 1 2 3 4 5 6 7 8 9 10 1 33 Granger M1 Variability Response to One S.D. Innovations Response of LNI to LNI Response of LNI to LNCP I Response of LNI to LNM1 Response of LNI to LNE R GDP
Granger 10 Granger Granger M1 2005 7 21 ECM M1 1 M1 3
M1 ( ) 1. Annie Koh & Richard Levich 1989. Synthetic Eurocurrency Interest Rate Futures Contracts: Theory and Evidence NBER Working Paper No. 3055*.Issued in August 1989. 2. BLACK F. DERMAN E. AND TOY W. 1990. A One-Factor Model of Interest Rates and its Application to Treasury Bond options Financial Analysts Journal 33-39 3. COURTADON G. 1982. The Pricing of Options on Default-Free Bonds Journal of Financial and Quantitative Analysis 17:75-100 4. Cox J. C. J. E. Ingersoll and S. A. Ross 1985. A Theory of the Term Structure of Interest Rates Econometrica 53 (1985) 385-407 5. DOTHAN L.U. 1978. On the Term Structure of Interest Rates Journal of Financial Economics 6:59-69 6. HEATH D. JARROW R. AND MORTON A. 1992. Bond
Pricing and theterm Structure of Interest Rates: A New Methodology for Contingent Claims Valuation Econometrica 60:77-105 7. Hull J. and A. White 1990. Pricing Interest Rate Derivative Securities. The Review of Financial Studies 3 (4). 8. Hull J. and White A.1993. One Factor Interest Rate Models and the valuation of Interest Rate Derivative Securities Journal of Financial and Quantitative Analysis 28 (1993) 235-254 9. Mankiw N. Gregory and Jeffrey A. Miron. 1986. The Changing Behavior of the Term Structure of Interest Rates. Quarterly Journal of Economics 101 (May): 211-28. 10. Swensen David F.2000. Pioneering Portfolio Management: An Uncoventional Approach to Institutional Investment The Free Pres. 11. Vasicek O.A.1997. An Equilibrium Characterization of the Term Structure Journal of Fianacial Economics 5 (1977) 177-188. 12. 2005 13. 2002 2002 01?14. 2005 2005 02 15. 2004 2004.12
16. 2005 2005 01 17. 2003 2003 10 1972.7 Journal of Finance 2004 2005